# Thread: Roll rates in RCVD

1. ## Roll rates in RCVD

Hello again!
I was wondering if you could help me. In RCVD, chapter 16, it does 2 examples, a full one and a simplified one. To calculate roll rates, it uses the following formula:
Roll rate= WH / (desired total roll gradient)

However, in the first example, W is the full weight of the car, but in the second one, it's only the sprung weight. Also, in this paper from OptimumG it uses the full weight too http://www.optimumg.com/docs/Springs...Tech_Tip_2.pdf

You get quite different results using both definitions, so I was wondering if you could help me. It seems to me that it's more logical to use the sprung weight for this calculation, since the springs and antiroll bars control the sprung weight, but I could use some guidance.

Jose Maria Martin
ARUS
University of Seville

2. 120 views and no responses

Anyway, I've kept doing ride and roll calculations (using the sprung weight for the case above) and I've run into some problems with the wheel displacement/frequency. I started out using a front frequency of 2,3 Hz as a baseline, and from that I calculated a ride rate, with the following data:
Full weight car+driver= 300 kg (I'm hoping for less, but just as an approximation)
Front weight distribution: 45%
Front unsprung weight: 26 kg
Front wheel sprung weight: 54,5 kg

So, Ride rate=4*pi^2*w^2*54,5=11382 N/m

On the other hand, I calculated the total load transfer, simply using
Load transfer to the outside wheels = Weight*Lat Accel*CG height/track=300*1,5*0,3/1,2= 112,5 kg
Which means that the front outside wheel should see a load increase of approximately 56.25 kg=551,8 N

Now I try to calculate how much suspension travel I would be using in that situation.
Wheel displacement = Load change/ride rate=551,8/11382=0,048 m = 48 mm
Which is way too much, ideally I'd like to be using less than 25 mm.

Now, my problem is that to solve that, I'd need to increase my front frequency (up to 3,1 Hz), thereby raising my rear frequency, and there comes a point when my rear ARB would need to produce negative roll stiffness to get the total lateral load transfer distribution I want. Either that, or choose a roll gradient under 0,9 deg/g, which is a bit low.

I guess that there are ways to work around this, but before that, I'd like to be sure that I haven't made some fatal mistake in my calculations.

Thank you very much for reading, and any comments will be appreciated!

Jose Maria Martin
ARUS Andalucia Racing
University of Seville

3. Jose,

Yes, I am one of those people who read your first post but didn't offer a reply.

This is because I consider the RCVD, OptimumG, and the general automotive-cottage-industry approach to this subject to be puerile codswallop. Along with this approach (ie. of "ride frequencies", etc.) being unnecessarily complicated, it lacks accuracy, and, worst of all, it is a great hindrance to good understanding of suspension design and Vehicle Dynamics generally. For more of my views you can Search posts with "Z", "front and rear ride frequencies", "interconnected suspension", etc., as keywords.

Perhaps a better approach for you is to continue studying the problem as a simple mechanical system that can be understood by the age-old methods of Classical Mechanics. Your above post suggests that you have a reasonable grasp of these methods, so proceed as you have above.

As a first approximation you might consider only a single "sprung mass", with the wheel-assemblies being massless. Later you can also consider the effects of the masses of the wheel-assemblies (so now five masses in total). Note that now with the same wheel-rates and same cornering Gs, different suspension kinematics result in different body-roll-angles. And there are also the gyroscopic effects to consider (as I posted somewhere, and which include the spinning engine parts...).

Very briefly, part of your second post above has the right approach (IMO). That is;
* You want high cornering Gs.
* You also want a narrow track (so you can squeeze more easily through the slaloms).
* So, it follows (from simple FBDs) that during cornering you want the car to almost (but NOT QUITE!) get up on its outside pair of wheels.
* So, almost (but not quite!) 100% of load is transfered from inside to outside wheels.
* So, if you only provide +/- 2.5 cm of vertical wheel travel (as is required by Rules), and you want a little bit of travel left for any bumps that might be in the corner, then your wheel-rates should be such that "static deflection" = ~ 2 cm (ie. the static wheel load (Fz) compresses the spring about 2 cm).
* So, for your front wheels, Wheel-rate = ~ 50 kg/2 cm = ~25 kg/cm (or ~25 kN/m, or ~25 N/mm).

And should you ever want to calculate any REAL resonant frequencies, then please use the methods of Classical Mechanics, rather than the cottage-industry codswallop in the automotive textbooks.

And, very importantly, FSAE CAN BE WON WITHOUT ANY SUSPENSION MOVEMENT AT ALL! So the above calculations are largely academic.

And ARBs are possibly the worst kinds of springs to put on a car. If you feel that you must stiffen the Roll-mode over the other suspension modes, then "longitudinal-Z-bars" are much better than "lateral-U-bars" (= ARBs).

Enough for now...

Z

4. Hi Z,
Thank you for your time and your comments. I've read some of the stuff you've referenced in the forums. I do agree with you that wheel ride displacement is a more useful way to choose ride rates. In my case, instead of choosing a natural frequency in a range that I read somewhere (2,5-3,5 Hz or whatever) it allows me to choose a ride rate that I actually want (as in, I know that I want my car, under high load cornering, to be using x mm of travel).

Your point about longitudinal-Z-bars, interconnected suspensions, and non-linear springs and bumpstops (I read that in another thread) are very interesting, and I will definitely look into that for next year's design. However right now it's too late to introduce new things in the design, I think it is more important to just build a car and test it.

On the other hand, I want to know as much as possible about vehicle dynamics, so I am gonna keep reading RCVD, OptimumG, and any other sources, to allow me to take my own decisions.

Thanks again,

Jose Maria Martin
ARUS Andalucia Racing
University of Seville

5. In the interests of a balanced discussion, I will counter some of Z's points.

The methods outlined in RCVD are simplifications and yes simplifcations require some cutting of corners. In this case, following the "traditional" method, you are largely constrained to end up with a traditional suspension with 4 springs and 2 anti roll bars. For passenger cars, this arrangement is a very good compromise between performance and complexity. Packaging anti roll bars is very simple. Packaging a longitudinal Z bar is a nightmare, and for what exactly?

At the end of the day, ANY model or method (including Z's) is necessarily a simplification and the traditional methods are quite a reasonable way to arrive at an adequate (but not optimum) solution without a lot of time or large amounts of input data. As you have mentioned, you don't have the time to do something out of the box so following a well established (and sucessful) route is a good choice from a risk management point of view. Even Z would agree, its more important to get the car built 1 month earlier than to agonise for 1 month more in the design phase about suspension rates.

The main problem though, from an educational point of view, is that often the traditional methods are taught as though they are the first principles of a suspension system whereas they absolutely are not. They are a (quite heavily reduced) simplification of how a suspension operates in roll and pitch. Additionally, they only have a limited range where they are valid (and this unfortunately does not include limit behaviour) and some suspension geometries cause the calculations to crash.

Your intuition should be telling you this anyway since these methods simply a complex system of 2 wheels + elastic tyres, 12-20 links located in 3D space, connected by a compliant chassis by compliant joints down into an equation with only 9 or so parameters (hrcF, hrcR, KwhlF, KwhlR, KrollF, KrollR, mass, mass_dist, cgh).

Regarding the book, there is too much good solid theory in RCVD (particularly the chapter on steady state stability and control) to simply brush it off as codswallop. My advice would be to follow whats in RCVD or in the Optimum G tips by all means but recognise you are cutting some corners by doing so.

6. Excellent response Tim! Good thread going on here..

7. To add to the debate of model accuracy.

""essentially, all models are wrong, but some are useful" - George E. P. Box
In Formula SAE, real racing, and the real world it is vital for us to understand how complex our simulations/models/calculations need to be. Is being more accurate providing more usefulness? Not necessarily. Is a more accurate model needed for someone just trying to learn the basics? Hell no. We can stroke our intellectual ego all day on this forum showing new and old FSAE people how brilliant we are, but what's the point? Make it useful. Make it work. Make sure you understand it. The conventional calculations that RCVD provides are certainly good enough for FSAE and really probably good enough for everything else. Now I know Z hates Claude, but I'm going to quote Claude on this one, "As engineers we work in deltas." Honestly it's not needed to get the calculations perfect as long as you're consistent. Get the car built. Test what is happening on the car. See what the difference is between real and theoretical. Make a setup change, see if the difference stays about the same. Make adjustments to the way you design the car the next year. Repeat.

8. Originally Posted by Z
Jose,
This is because I consider the RCVD, OptimumG, and the general automotive-cottage-industry approach to this subject to be puerile codswallop.
Z
To Z,

Since you write your blames on the public place and name me, I have to ask you publicly: What did I do to you to deserve such a brutal language?

9. Thank you for all your responses, it's been really useful. I know about models being just that, models, and only representing reality up to a point. I was just worried that I had done some stupid mistake in my calculations, and my results were going to be way off haha
Anyway, I am still inmersed in my excel worksheets, I wanna make sure I get some consistent results and then go and build the car!

Jose Maria Martin
ARUS Andalucia Racing
University of Seville

10. Jose,

"120 views and no responses."

Better now?

(More for you below...)
~~~~~o0o~~~~~

Tim,

"In the interests of a balanced discussion, I will counter some of Z's points."

Thank you. I like balanced discussions too.
~o0o~

"...following the "traditional" method, you are largely constrained to end up with a traditional suspension with 4 springs and 2 anti roll bars. For passenger cars, this arrangement is a very good compromise between performance and complexity. Packaging anti roll bars is very simple. Packaging a longitudinal Z bar is a nightmare, and for what exactly?"

The "for what" answer is that Longitudinal-Z-Bars give FAR SUPERIOR PERFORMANCE. Especially so on bumpy roads, but also on moderately undulating roads. So, realistically, for all real roads. Very briefly, the soft Twist-mode possible means that wheel Fz loads change much less with the (very common) twist in the road, hence giving much better grip, more consistent handling, more comfortable ride, etc+++.

Until suspension engineers physically experience this, they will never appreciate it. As you say, the traditional method guarantees a stiff Twist-mode (which comes mainly from the ARBs). The traditional response to the poor performance is simply to blame the road for being too bumpy.

As for the "nightmare" of packaging Long-ZBs, well, you must have funny dreams! [<- Said in humorous tone.] I have promised some students who have PM'd me that I will do some more sketches on this soon, and they will happen... (yes, Tax Return finally done, and only 9 months late!).

Again briefly, there are, and have been, a great many cars that already have half of the Long-ZBs packaged. These are the cars with longitudinal-torsion-bar front-suspensions (eg. many late 1900s Chryslers, Renaults++, current Toyota Hiluxes++). Adding similar size torsion-bars rotated 180 degrees and connected to the rear suspensions, with the two bars on each side joined in the middle of the car, gives the required Long-ZBs. Easy packaging! See the 1950s Packard for the general layout.
~o0o~

"At the end of the day, ANY model or method ... is necessarily a simplification ...
Even Z would agree, its more important to get the car built 1 month earlier than to agonise for 1 month more in the design phase about suspension rates."

This is exactly my point.

The first paragraph of the OptimumG tip (linked by Jose) tells you to FIRST "pick a ride frequency", and then "calculate spring rate needed for the chosen frequency". So after agonising for months over your chosen (and fictional!) frequency, you still have to go through several pages of equations to get the spring-rates. My suggested approach can be done in a moment, and all in your head. Namely, wheel-rate = corner weight/chosen-suspension-displacement. Next, off for some testing...
~o0o~

"My advice would be to follow whats in RCVD or in the Optimum G tips by all means but recognise you are cutting some corners by doing so."

NOT "cutting corners", but rather taking a long, and circuitous, and difficult route through the blackberry-bushes, when the same answer is just a step away.
~~~~~o0o~~~~~

Trent,

"The conventional calculations that RCVD provides are certainly good enough for FSAE and really probably good enough for everything else."

As above. The "conventional calculations" introduce a fictional detour through the Fairytale Land of Frequencies, when no such detour is required! Why? Why bother?? What word is more suitable to describe this detour than "codswallop"???

Anyway, all this is due to the commonly held H. Sapien view that "progress" is all about making things more complicated, and difficult, and useless. Like bureaucracies, and Tax Returns, and the FSAE Rulebook...
~o0o~

"Now I know Z hates Claude..."

No, no, no, no, noooo...
~~~~~o0o~~~~~

Claude,

I DO NOT hate you. Not at all!

However, in 2002 I tried to enlighten you regarding some issues of Classical Mechanics, issues that would have helped both your understanding of Vehicle Dynamics, as well as all of the students (and industry professionals?) that you have taught since then. More recently on this Forum I have tried to do the same, and also to make you aware of many other issues (eg. interconnected suspensions) that you appear to currently not be aware of. For reasons that you only know, you have ignored this help, and, in fact, not even shown any interest in discussing it openly, or learning it for yourself.

I find this rather dissappointing. Mainly because your efforts make the next generation of young Engineers LESS knowledgable. It is all of future society that then pays the big price (ie. of undereducated Engineers who believe in "magic numbers", voodoo, whatever else...). Not me or you.
~o0o~

"What did I do to you to deserve such a brutal language?"

"Puerile codswallop" translates as "childish silliness/nonsense". Not too brutal?
~~~~~o0o~~~~~

Jose (again),

For your Spring-Damper design I suggest you look at U of Cincinnati's 2013 car (see links and discussion by Matt (mdavis) on the "FSAE Lincoln 2013" thread, in the Competitions section). They had direct-acting SDs (like Monash, winner of 2013-Oz), no ARBs, rubber spacers for spring-rate adjustments, and they did quite well! At most you might need three sets of springs (soft, medium, and stiff), with my earlier "static displacement" calc getting you in the ball-park for these rates.

With spring-rates solved, I then much more strongly suggest that you concentrate on controlling your suspension's toe and camber compliances, and get the car built ASAP so that you can start optimising the "nut on the end of the wheel" (ie. driver development!).

Z